9 problems

Consider the stochastic two-dimensional Navier–Stokes equations on the torus with additive noise applied only to a degenerate collection of Fourier modes. The viscosity is denoted…

Let a fluid dynamics model with zero initial datum possess infinitely many weak solutions. Couple it with a transport equation and subject the velocity field to multiplicative and…

Let $N^\nu$ be a positive frequency scale and let $(\theta^\nu)_{\nu\in(0,1)}$ be a family of noise coefficients such that … Assume that anomalous dissipation of energy holds for t…

Let $\theta^\nu$ denote the viscosity-dependent transport-noise coefficients in the two-dimensional stochastic velocity equation. The cited theorem uses a particular scaling of…

Let $theta^ u=(thetak^ u){kinmathbb Z0^2}$ be the noise coefficients, and write … The notation $|k|\eqsim\nu^{-\delta}$ means that the active frequencies are comparable to…

Forcing-independence conjecture. The large deviations principle for the system holds independently of the choice of the forcing $f\in L^2(0,T;H_0)$; equivalently, if an LDP holds f…

Let $W$ be a noise satisfying Assumption … {rm d} omega + operatorname{curl}^{-1} omegacdot nabla omega, {rm d} t + circ {rm d} Wcdot nabla omega = 0 … such that these stochastic 2…

The KIW formula describes the stochastic evolution of a time-dependent $k$-form under stochastic transport, with its final expression being coordinate free. A manifold is a space o…

Let p^{\nu,\kappa}({\text{\boldmath x}}',0\mid{\text{\boldmath x}},t_f) be the particle transition probability density at viscosity $\nu$ and scalar diffusivity $\kappa$, and…